# Question: Xiang Zhu a client of FinCorp Inc has phoned you

Xiang Zhu, a client of FinCorp Inc., has phoned you with a question. She has been reading a finance textbook and cannot understand how to use the binomial option pricing model to value a call option. The underlying stock is currently trading for \$100. There is a 30-percent chance it will increase to \$190 in one year, and a 70-percent chance it will fall to \$85 in the same period. The risk-free rate is 10 percent. There is a call option with a strike price of \$170, which according to the binomial model should have a value of \$4.329. Xiang is confused because she calculates that if there is a 30-percent chance the call will be worth \$20 and a 70-percent chance it will be worth zero, the expected value should be \$6. Why is it only worth \$4.329?
a. Demonstrate that if the call was trading for \$6, there would be an arbitrage opportunity.
b. Calculate the risk-neutral probabilities.
c. Calculate the expected present value of the call option using the risk-neutral probabilities.
d. Why can we value options as if the investors are risk neutral?

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